Question

Forming Triple integral
z=0, z=1, x^2 +y^2 =4

Answer 1

limits for x will be ?? ...if i want \(\int \int \int 2z dxdydz\)

Answer 2

i mean i first want to integrate w.r.t x

limits for z are easy, 0 to 1
but x and y...

Answer 3

x=-4 to 4

y = -sqrt(4-x^2) to sqrt(4-x^2)

assuming cartesian

Answer 4

that would cover a circle in xy plane, right ?

Answer 5

yes

Answer 6

radius is 2 , so from -2 to 2, right ?

Answer 7

lol, yeah

Answer 8

wait, but i will get a 0!

Answer 9

z will be constant when i integrate w.r.t x
so,
integral -2 to 2 of dx = 0

Answer 10

going for symmetry, x = -2 to 2, y = 0 to sqrt(4-x^2)

you want dx dy dz? or some other order?

Answer 11

any order is fine

Answer 12

dx dy dz .... would have to rework the movements

Answer 13

just want to triple integrate 2z over the volume formed by that cylinder

Answer 14

z = 0 to 1
y = -2 to 2
x = sqrt(4-y^2) to -sqrt(4-y^2)

2z dx = 2z(xb-xa) = 4zsqrt(4-y^2)